Description: Lemma for bfp25947.
The sequence , which
simply starts from any
point in the space and iterates , satisfies the property that
the distance from to decreases
by at least
after each
step. Thus the total distance from any
to is bounded by a geometric series, and the sequence is
Cauchy. Therefore, it converges to a point
since the space is complete. (Contributed by Jeff Madsen,
17-Jun-2014.)